Apparatus and method for reducing phase noise in oscillator circuits

ABSTRACT

A resonant oscillator circuit includes an active device and a resonator that causes the active device to oscillate at a resonant frequency of the resonator. The active device includes one or more transistors that are DC biased using one or more resistors. The bias resistors generate thermal noise that is proportional to the resistance value. An external inductor circuit is connected across the output terminals of the active device and in parallel with the resonator. The external inductor circuit short-out at least some of the thermal noise that is generated by the bias resistors, and thereby reduces the overall phase noise of the resonant oscillator.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. appl. Ser. No. 09/783,033,filed on Feb. 15, 2001 now U.S. Pat. No. 6,437,652 which claims thebenefit of U.S. Provisional Application No. 60/258,492, filed on Dec.29, 2000, which is incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to phase noise reduction inoscillator circuits, and more specifically to phase noise reduction indifferential crystal oscillator circuits.

2. Background Art

Radio frequency (RF) transmitters and receivers perform frequencytranslation by mixing an input signal with a local oscillator (LO)signal. Preferably, the LO signal should have a frequency spectrum thatis as close to a pure tone as possible in order to maximize systemperformance during the signal mixing operation. The deviation of the LOsignal from a pure tone is quantified as phase noise or phase jitter,and is generally referred to as spectral purity. In other words, a LOsignal with good spectral purity has low phase noise.

Typically, the LO signal is generated from a lower frequency referencesignal in order to maximize spectral purity. The lower frequencyreference signal is often frequency multiplied to generate the higherfrequency LO signal. For instance, a phase lock loop (PLL) generates anoutput signal that is a frequency multiple of an input reference signal,but is phase-locked to the input reference signal. In some applications,several multiplication stages are required to achieve the desired LOfrequency.

Frequency multiplication can negatively impact spectral purity byincreasing phase noise in the output LO signal. Phase noise increasesbecause frequency multiplication (which is equivalently phasemultiplication) enhances phase noise spectral density as the square ofthe multiplication factor. Therefore, the higher order multiplication ofa noisy reference signal is to be avoided.

A crystal oscillator is often used to generate the reference signalbecause of its inherently low phase noise attributes. A crystaloscillator includes an active device and a crystal, where the impedanceof the crystal is a short (or an open) circuit at a natural resonantfrequency. By connecting the crystal in parallel with the active device,a positive feedback path is created between the oscillator terminals atthe crystal resonant frequency. The positive feedback causes the activedevice to oscillate at the crystal resonant frequency.

A crystal resonator has a relatively high quality factor, or “Q”, whencompared to other types of resonators. Therefore, the bandwidth of thecrystal resonance is relatively narrow so that the impedance change ofthe crystal in the vicinity of its resonant frequency is relativelyabrupt. The relatively high Q of the crystal improves the spectralpurity of a crystal oscillator output signal because the crystalresonance determines the frequency of oscillation for the active devicein the oscillator. Accordingly, a crystal oscillator has a relativelylow phase noise compared to other resonant oscillator configurations.

The active device in the crystal oscillator typically includes one ormore transistors that can be configured in various arrangements.Transistors necessarily require some type of bias circuitry to power thetransistors. The bias circuitry typically includes one or moreresistors, which inherently produce thermal noise that is proportionalto the total resistance. The thermal noise voltage modulates the zerocrossings of the oscillation waveform, and increases the phase noisefloor around the oscillation frequency. The increased phase noise floordetracts from the inherently low phase noise of a crystal oscillator.Additionally, as stated above, a high phase noise floor is undesirablein reference signals that drive frequency synthesizers because theoutput phase noise increases with square of any frequency multiplicationthat is performed by the synthesizer.

Therefore, what is needed is an oscillator circuit architecture thatnullifies the thermal noise voltage that is created by the biasresistors that power the active device in the oscillator circuit.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to an external inductor circuit thatreduces phase noise in a resonant oscillator circuit. The externalinductor circuit provides a DC path across the oscillator outputterminals and shorts-out thermal noise that is generated by theoscillator circuit, thereby preventing the thermal noise from increasingthe phase noise floor of the oscillator output signal.

A resonant oscillator circuit includes an active device and a resonator,such as a crystal resonator. The resonator causes the active device tooscillate at the resonant frequency f₀ of the resonator by creatingpositive feedback (or negative resistance) in the active device at theresonant frequency f₀.

The active device includes one more transistors that require DC biascircuitry to provide power for the transistors. The DC bias circuitrytypically includes one or more resistors that generate thermal noisethat increases in proportion to the total resistance. The externalinductor circuit is connected across the terminals of the oscillatorcircuit, and in parallel with the resonator. The external inductorcircuit shorts-out the thermal noise from the resistors so the thermalnoise does not increase the phase noise floor of the oscillator outputsignal.

The external inductor circuit includes an inductor and a resistorconnected in series, which provide the DC path that shorts-out thethermal noise from the bias resistors. The value of the inductor issufficiently large so as not to interfere with the positive feedbackpath that is created by the resonator at the resonant frequency f₀. Inother words, the parallel combination of the inductor and the resonatorshould not substantially shift the resonant frequency f₀ of theresonator, so as not to change the operating frequency of theoscillator. This can be accomplished by assuring that any parasiticresonance caused by the external inductor is sufficiently lower infrequency than the intended resonant frequency of the resonator.

The value of the resistor is sufficiently large to suppress any unwantedparasitic oscillations that are caused by the external inductorresonating with the resonator capacitance. However, the resistor in theexternal inductor circuit should be no larger than necessary as it willgenerate its own thermal noise that is proportional to the resistorvalue just like the bias resistors for the active device. Inembodiments, the resistor value is no larger than the bias resistorsassociated with the active device.

Further features and advantages of the present invention, as well as thestructure and operation of various embodiments of the present invention,are described in detail below with reference to the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

The present invention is described with reference to the accompanyingdrawings. In the drawings, like reference numbers indicate identical orfunctionally similar elements. Additionally, the left-most digit(s) of areference number identifies the drawing in which the reference numberfirst appears.

FIG. 1A illustrates an oscillator configuration;

FIG. 1B illustrates an ideal oscillator output signal that does notinclude phase noise;

FIG. 1C illustrates an oscillator output signal that does include phasenoise;

FIG. 2A illustrates a series resonant circuit;

FIG. 2B illustrates a parallel resonant circuit;

FIG. 2C illustrates a crystal resonator;

FIG. 2D illustrates an equivalent circuit for a crystal resonator;

FIG. 2E illustrates a crystal resonator having an additional capacitancein parallel with the crystal resonator;

FIG. 2F illustrates an equivalent circuit for the crystal resonatorhaving the additional capacitance;

FIG. 3A illustrates an impedance plot for a series resonant device;

FIG. 3B illustrates an impedance plot for a parallel resonance device;

FIG. 3C illustrates an impedance plot for a crystal resonator having aseries resonance and a parallel resonance;

FIG. 4 illustrates various resonant circuit impedance plots fordifferent Q values;

FIG. 5 illustrates a synthesizer that is driven by a oscillator;

FIG. 6 illustrates an oscillator 600 that has an external inductorcircuit to short-out thermal noise that is generated by the oscillatorbias resistors according to embodiments of the invention;

FIG. 7 illustrates a flowchart 700 that further describes the operationof the oscillator 600;

FIG. 8 illustrates a differential crystal oscillator 800 according toembodiments of the present invention;

FIG. 9 illustrates the differential crystal oscillator 800 with anexternal inductor circuit to short-out thermal noise that is generatedby the oscillator bias resistors according to embodiments of the presentinvention; and

FIG. 10 illustrates an alternate embodiment for the external inductorcircuit according to embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

1. Oscillator Configuration

FIG. 1A illustrates an oscillator circuit 100 having a resonator 102, anactive device 104, and at least one resistor 106 to bias the activedevice 104. The oscillator 100 generates the output signal 112 that ispreferably a pure tone in the frequency domain at the resonant frequencyf₀ of the resonator 102, as shown in FIG. 1B.

Realistically, the output signal 112 is not a pure tone because of thephase noise that is associated with the oscillator circuit 100. As shownin FIG. 1C, the phase noise manifests itself as energy “skirts” 114around the oscillation frequency f₀. To quantify phase noise, the noisepower in a unit frequency bandwidth 116 is determined at an offset 118from the resonant frequency f₀. The measured noise power in bandwidth116 is then divided by the average total power in the output signal 112to calculate a value for the phase noise.

The active device 104 is capable of oscillating when there is positivefeedback (or a negative resistance) between an input terminal 108 and anoutput terminal 110. For instance, the active device 104 can include oneor more transistors that have sufficient gain at the frequency ofinterest to oscillate. Exemplary transistors include a field effecttransistor (FET) and a bipolar junction transistor (BJT). Inembodiments, the active device 104 is configured to include across-coupled differential pair of transistors, which is describedfurther herein.

The resonator 102 is connected across the terminal 108 and the terminal110 of the active device 104, and has an impedance that approaches ashort circuit or an open circuit at the resonant frequency f₀. Forexample and without limitation, the resonator 102 can be a series LCcircuit 201 (FIG. 2A), a parallel LC circuit 207 (FIG. 2B), or a crystal214 (FIG. 2C), all of which are described in further detail below. Atthe resonant frequency f₀, the resonator 102 causes the positivefeedback that is required for the active device 104 to oscillate andproduce the output signal 112.

The series LC circuit 201 has an inductor 202, a capacitor 204, and aparasitic resistor 206 that are connected in series. The impedance ofthe LC circuit 201 is depicted in FIG. 3A. As shown in FIG. 3A, theimpedance of the LC circuit 201 approaches 0 ohms at the resonantfrequency f₀, as this is the frequency where the impedance of theinductor 202 and the capacitor 204 cancel each other. The resonantfrequency f₀ is determined according to the following equation:

f ₀=(½π)·1/sqrt(LC)  Eq. 1

Ideally, the resistance of the parasitic resistor 206 is 0 ohms, inwhich case the impedance of the LC circuit 201 would be 0 ohms at theresonant frequency f₀. Practically, the resistance of the parasiticresistor 206 is non-zero, and therefore the resistance of the LC circuit201 at f₀ is not 0 ohms. The quality factor (or “Q”) quantifiesbandwidth (or “sharpness”) of the resonance based on the ratio of thecircuit reactance and the parasitic resistance according the equation:

Q=(2πf ₀ L)/R  Eq. 2

As shown by Eq. 2, Q increases for the series LC circuit 201 as theresistance R decreases. Correspondingly, the oscillator Q and spectralpurity also increases as the resistance R decreases.

Referring to FIG. 2B, the parallel LC circuit 207 has a capacitor 208,an inductor 210, and a resistor 212 that are connected in parallel. Theimpedance of the LC circuit 207 is depicted in FIG. 3B. As shown in FIG.3B, the impedance of the LC circuit 207 approaches an open circuit atthe resonant frequency f₀, as this is the frequency where the admittanceof the inductor 210 and the capacitor 208 cancel each other out.Ideally, the parasitic resistor 212 is infinite (i.e. an open circuit),in which case the impedance of the LC circuit 207 would be an ideal opencircuit at the resonant frequency f₀. Practically, the parasiticresistor 212 is a not infinite, and therefore the impedance of the LCcircuit 207 at f₀ is not infinite. Q for a parallel LC circuit isdetermined according to the following equation:

Q=2πf ₀ RC  Eq. 3

As shown by Eq. 3, Q increases for the parallel LC circuit 201 as theresistance R increases. Correspondingly, the oscillator Q and spectralpurity also increases as the resistance R increases.

The crystal 214 has a reciprocal relationship (called the piezoelectriceffect) between the mechanical deformation along one crystal axis andthe appearance of an electrical potential along a second crystal axis.Therefore, deforming a crystal will separate charges and produce avoltage at the crystal terminals. Conversely, an applied voltage acrossthe crystal will deform the crystal. If the applied voltage issinusoidal with a variable frequency, then the crystal will go intomechanical oscillation, and exhibit a number of resonant frequencies.

The crystal 214 has an equivalent electrical circuit 216 that is shownin FIG. 2D. LC circuit 216 includes a series resonant circuit 217 thatrepresents the equivalent circuit corresponding to the piezoelectriceffect for the crystal 214 that was described above. The series resonantcircuit 217 includes a motional inductor L_(M) 219, a motional capacitorC_(M) 220, and a motional resistor R_(M) 222. Additionally, the LCcircuit 216 has a package capacitance C_(P) 218 that represents thecapacitance associated with the electrical package that the crystal ismounted in.

The impedance plot for the crystal equivalent circuit 216 is shown inFIG. 3C. As shown in FIG. 3C, the impedance plot includes a firstresonance 302 and a second resonance 304. The first resonance 302 is aseries resonance that occurs at the frequency where the impedance of theL_(M) 219 and the C_(M) 220 cancel each other, and can be calculated byusing Eq. 1. The second resonance 304 is a parallel resonance thatoccurs at the frequency where the admittance of the series resonantcircuit 217 and the admittance of the C_(P) 218 cancel each other, whichcan be determined by using Eq. 5 herein.

In radio frequency applications, 10 MHZ is a popular referencefrequency. However, standard value commercially available crystals arenot resonant at 10 MHZ without adding an additional capacitance 224 inparallel with the crystal 214 as shown in FIG. 2E. FIG. 2F illustratesthe equivalent circuit 225 of the crystal resonator 214 with the addedcapacitance 224. The additional capacitance 224 can be varied to tunethe parallel resonance 304 to a desired frequency (e.g. 10 MHZ) bychanging the total parallel capacitance of the equivalent circuit 225.

The Q of a crystal is typically substantially higher than resonatorsthat are comprised of discrete circuit elements (i.e. discrete inductorsand capacitors). For example, FIG. 4 illustrates several impedancecurves 402 for resonant LC circuits having different Q values. Referringto FIG. 4, the curves 402 a-c are representative of LC circuits that aremade of discrete components, such as LC circuits 201 and 207 describedherein. Whereas, the curve 402 d is representative of a crystal, such ascrystal 214. As shown, the crystal impedance curve 402 d has asubstantially sharper resonance at the resonant frequency (1.0 MHZ inthis example) when compared to the other impedance curves 402 a-c. Thisoccurs because the ratio of the motional resistance (R_(M) 222) to themotional reactance (L_(M) 219 and C_(M) 220) of the crystal 214 is muchsmaller than the ratio of the parasitic resistance to the reactance ofthe lumped LC circuits 201 and 207.

As mentioned above, the bias resistor 106 represents one or moreresistors that bias the active device 104. The active device 104typically includes one or more transistors and incorporates the biasresistor 106 to provide DC power for the transistors. The bias resistor106 can be integrated within active device 104 depending on the specificcircuit configuration that is utilized, as will be understood by thoseskilled in the relevant arts. The bias resistor 106 generates thermalnoise voltage that increases with increasing temperature, resistance,and circuit bandwidth according to the following equation:

 V _(n) ²=4kTRB,  Eq. 4

where:

T=temperature in kelvin

R=resistance

k=Boltzmann's constant

B=bandwidth in hertz.

The thermal noise from the resistor 106 modulates the zero crossing ofthe output signal 112 of the oscillator 100. Since the output signal 112is hard limited in the oscillator 100 (because to the oscillator 100 isin saturation), the thermal noise from the resistor 106 leads to higherphase noise in the output signal 112. As shown in FIG. 1C, the phasenoise manifests itself as energy “skirts” 114 in the output signal 112around the resonant frequency f₀.

Phase noise is undesirable in reference signals that are the basis forfrequency multiplication. For instance, FIG. 5 illustrates theoscillator 100 driving a synthesizer 502 to generate a LO signal 506.The synthesizer 502 includes a multiplier 504 that multiplies thefrequency of the oscillator output signal 112 by a factor of N, togenerate the LO signal 506 that is used for frequency mixing in a mixer508. Frequency multiplication (which is equivalently phasemultiplication) enhances phase noise spectral density as the square ofthe multiplication factor, so that higher order multiplication of anoisy reference signal should be avoided. More specifically, phase noisedensity in the LO signal 506 will increase as a factor of N², where Nrepresents the amount of frequency multiplication. The mixer 508down-converts a RF signal 510 by frequency mixing the RF signal 510 withthe LO signal 506 to generate an IF signal 512.

2. Phase Noise Reduction in Oscillator Circuits

FIG. 6 illustrates an oscillator 600 according to embodiments of thepresent invention. The oscillator 600 is similar to the oscillator 100except that the oscillator 600 includes a feedback circuit 602 that isconnected across the active device 104. The feedback circuit 602 isconnected in parallel with the resonator 102 across the terminals 108and 110 of the active device 104. The feedback circuit 602 includesinductor 604 and a resistor 606.

The feedback circuit 602 provides a DC path from the terminal 108 to theterminal 110 for any thermal noise that is generated by the biasresistor 106. As such, the thermal noise from the bias resistor 106 isshorted-out and does not increase the phase noise floor of the outputsignal 112. The feedback circuit 602 is redundant if the resonator 102is the parallel LC configuration 207 (FIG. 2B) because the inductor 210already provides a DC path across the terminals 108 and 110. However,the feedback circuit 602 is not redundant if the resonator 102 is theseries LC configuration 201 (FIG. 2A) because the capacitor 204 operatesas a DC block that prevents DC and low frequency energy from passingthrough the resonator 201. Additionally, the feedback circuit 602 in notredundant for the crystal 214 because the C_(P) 218 and the C_(M) 220(shown in the equivalent circuit 216) also operate as a DC block thatblocks the feedback of DC and low frequency energy.

In addition to nullifying thermal noise, the inductor 604 in theinductor circuit 602 combines with the parallel capacitance in theresonator 102 to cause an (unwanted) low frequency parasitic resonance.For instance, in the crystal 214, the inductor 604 combines with C_(P)218 (or the parallel combination of C_(P) 218 and C_(ADD) 224) to causean (unwanted) low frequency parasitic resonance. Preferably, the valueof the inductor 604 is sufficiently large so this parasitic resonancedoes not shift the oscillation frequency of the oscillator 600 from theresonant frequency f₀ of the resonator 102. The inductor 604 should beselected so as not interfere with the feedback path provided by theresonator 102 at the resonant frequency f₀. Accordingly, the parallelcombination of the inductor 604 and the resonator 102 should notsubstantially shift the resonant frequency f₀ of the resonator 102, soas not to change the operating frequency of the oscillator 600. This canbe accomplished by assuring that the parasitic resonance that is causedby the inductor 604 is lower than the frequency of the desired resonanceof the resonator 102 by approximately a factor of {square root over(10)}. In other words, the parasitic resonance occurs at a frequencythat is approximately {square root over (0.1)} of the frequency of thedesired resonance, or lower. For example and without limitation,assuming that the resonator 102 has an intended resonance at 10 MHZ,then the parasitic resonance caused by the inductor 604 shouldpreferably be approximately 3 MHZ, or less. For a given capacitancevalue, a minimum value for the inductor 604 can be determined fromEq. 1. Assuming that the resonator 102 has an equivalent capacitance of20 pF, then the value of the inductor 604 should be approximately 100 μH(or greater) in order to assure that the parasitic resonance is at 3 MHZor below. Note that if the additional capacitance 224 (FIG. 2E) isutilized for tuning the crystal resonance, then the capacitance that isused to calculate the inductor 604 is the parallel combination ofC_(ADD) 224 and C_(P) 218.

The resistor 606 dampens out any unwanted parasitic oscillations thatare caused by the addition of the inductor 604. The parasiticoscillations correspond to the parasitic resonance that was describedabove for the inductor 604. It is preferable to suppress these parasiticoscillations even if the parasitic oscillation frequency is far removedfrom the intended oscillation frequency because the parasiticoscillations will divert signal power from the intended oscillationfrequency, possibly to the extent of completely suppressing the intendedoscillation. Additionally, the parasitic oscillations will frequency mixwith intended oscillation frequency, and generate spurious signals inthe output oscillator signal 112, which reduces overall spectral purity.

The value of the resistor 606 should be sufficiently large to suppressthe unwanted oscillations that are associated with the inductor 604.However, the resistor 606 should be no larger than necessary as theresistor 606 generates unwanted thermal noise that increases with theresistance value according to Eq. 4. The thermal noise of the resistor606 increases the phase noise of the oscillator output signal 112 justlike the bias resistor 106, and therefore defeats the purpose of thefeedback circuit 602 if the resistor 606 is too large. The exact valueof the resistor 606 will depend on the specific application, circuitconfiguration, and active device gain, as will be understood by thoseskilled in the relevant arts. In embodiments, the value of the resistor606 should be less the value of the bias resistor 106. In embodiments,the resistor 606 is a potentiometer (i.e. variable resistor), whichallows for a variable amount of resistance to be added to or subtractedfrom the feedback circuit 602. In alternate embodiments, the resistor606 is a fixed resistor.

The flowchart 700 further describes the operation of the oscillatorcircuit 600, and phase noise reduction according to the presentinvention. The order of the steps in the flowchart 700 is not limitingas some (or all) of the steps can be performed simultaneously or in adifferent order, as will be understood by those skilled in the relevantarts.

In step 702, the resonator 102 causes the active device 104 to oscillateat the resonant frequency f₀ of the resonator 102, generating the outputsignal 112 that is preferably a pure tone at f₀. The resonator 102provides a positive feedback path for the active device 104 at theresonant frequency f₀, thereby causing the active device 104 tooscillate at f₀. The resonator 102 can be anyone of the resonators thatare shown in FIGS. 2A-2F, or other resonators that will be apparent tothose skilled in the relevant arts based the discussion given herein. Ina preferred embodiment, the crystal 224 is the resonator of choicebecause of its superior Q as described herein.

In step 704, the bias resistor 106 generates thermal noise. Themagnitude of the thermal noise voltage increases with temperature,resistance, and circuit bandwidth, according to Eq. 4.

In step 706, the external inductor circuit 602 shorts out at least someof the thermal noise that is generated by the bias resistor 106, andprevents this thermal noise from increasing the phase noise floor of theoscillator output signal 112. More specifically, the inductor 604 andthe resistor 606 provide a DC feedback path (and a low frequencyfeedback path) between the terminals 108 and 110 of the active device104. The resistor 606 dampens out any parasitic oscillations that arecaused by the inductor 604 resonating with the capacitance in theresonator 102.

In step 708, the additional capacitance C_(ADD) 224 can be tuned toadjust the center frequency of the oscillator 600. When the crystal 214is used as the resonator 102, the capacitance 224 is often added inparallel with the crystal 214 to fine tune the oscillator frequency. Ifthe DC feedback circuit 602 causes the oscillator frequency to shift,then the capacitance 224 can be adjusted to compensate for the frequencyshift.

FIG. 10 illustrates an oscillator circuit 1000 that has an alternateconfiguration for the external inductor circuit. More specifically, theoscillator circuit 1000 has an external inductor circuit 1002 with tworesistors 1004 a and 1004 b, in addition to the inductor 604. Theresistors 1004 are approximately ½ of the value of the resistor 606 thatis shown in FIG. 6.

3. Differential Crystal Oscillator and Phase Noise Reduction

FIG. 8 illustrates a differential crystal oscillator 800 as oneembodiment of the crystal oscillator 100. The differential crystaloscillator 800 is meant for example purposes only and is not meant tolimit the invention in any way. Other oscillator configurations could beutilized to practice the invention, as will be understood by thoseskilled in the relevant arts based on the discussions given herein.

The differential crystal oscillator 800 includes a current source 802,an active device 804, bias resistors 810 a and 810 b, an active biascircuit 812, and a crystal resonator 214. The active device 804oscillates at the resonant frequency f₀ of the crystal 214, to produce adifferential output signal 821 that can be taken across the nodes 820 aand 820 b. The active bias circuit 812 and the bias resistors 810provide DC bias for the active device 804. The structure and operationof the differential crystal oscillator 800 is discussed in furtherdetail as follows.

The active device 804 includes cross-coupled transistors 806 a and 806 bthat oscillate at the resonant frequency of the crystal 214. The drainof transistor 806 a is coupled to the gate of transistor 806 b through acapacitor 808 a. Likewise, the drain of transistor 806 b is coupled tothe gate of the transistor 806 a through a capacitor 808 b. This crosscoupled arrangement provides a feedback path for AC signals that passthrough the capacitors 808. The crystal 214 is coupled across the nodes820 a and 820 b, which are also the drains of the respective transistors806 a and 806 b. As such, the crystal 214 is coupled in parallel withfeedback path for the cross coupled transistors 806 a and 806 b. Atresonance, the impedance of the crystal 214 becomes an open circuit, andcauses a positive feedback condition to exist between the transistors806 at the resonant frequency f₀ of the crystal 214. The positivefeedback causes the transistors 806 to oscillate at the resonantfrequency f₀ of the crystal 214, and produce the differential outputsignal 821 that can be taken across the nodes 820 a and 820 b. Thecapacitors 818 a and 818 b are used to tune to the output frequency ofthe crystal oscillator 800, and therefore function as the capacitorC_(ADD) 224 in FIG. 2F.

The transistors 806 are not directly coupled to each other because doingso would cause the transistors to latch-up. In other words, onetransistor 806 would turn-on all the way and the other transistor 806would be cutoff, preventing the desired oscillation. The capacitors 808prevent the lock-up condition by blocking DC feedback between therespective gates and drains of the transistors 806.

The active bias circuit 812 includes two diode connected transistors 816a and 816 b. The resistor 814 a connects the drain and gate of thetransistor 816 a to form the diode connection for the transistor 816 a.The resistor 814 b connects the drain and gate of the transistor 816 bto form the diode connection for transistor 816 b. The diode connectedtransistors 816 a and 816 b provide a stable common mode drain voltageat nodes 820 a and 820 b, based on the current source 802.

The bias resistors 810 a and 810 b are also connected to the nodes 820 aand 820 b (through the resistors 814) and provide gate bias voltage forthe transistors 806. More specifically, the resistor 810 a provides DCbias for the gate of the transistor 806 b, and the resistor 810 bprovides DC bias for the gate of the transistor 806 a.

As shown, the bias resistors 810 are also connected to the feedbackcapacitors 808, and shunt away some of the feedback signal that is meantfor the transistors 806, thereby reducing the overall gain of thetransistors 806. If the gain is reduced too much, then the positivefeedback will be quashed, and the transistors 806 will not oscillate asintended. Therefore, the resistors 810 should be relatively large tomaintain the gain of the active circuit 804. In embodiments, the valueof the resistors 810 are in the 10 k ohm range, but other resistorvalues could be utilized as will be understood by those skilled in therelevant arts. The bias resistors 810 generate thermal noise voltagethat increases with their resistance value according to the Eq. 4. Asdiscussed herein, this thermal noise voltage is undesirable because itincreases the phase noise floor of the oscillator output signal.

The differential crystal oscillator 800 is further described in U.S.patent application entitled, “Differential Crystal Oscillator”, Ser. No.09/438,689, filed on Nov. 12, 1999, Attorney docket no. 33758/LTR/B6,which is incorporated herein by reference in its entirety.

FIG. 9 illustrates the oscillator 800 with the inductor circuit 602connected across the output nodes 820 a and 820 b of the oscillator 800.The inductor circuit 602 is also in parallel with the crystal 214. Theinductor circuit 602 provides a DC feedback path across the output nodes820 a and 820 b for any thermal noise from the bias resistors 810 andthe feedback resistors 814. As such, the thermal noise from the biasresistors 810 and the feedback resistors 814 is shorted-out and doesincrease the phase noise of the oscillator output signal 821.

As stated above, the inductor circuit 602 is in parallel with thecrystal 214. Therefore, the inductor 604 can resonant with theequivalent capacitance of the crystal 214 to cause an (unwanted)parasitic resonance. For instance, the inductor 604 could resonate withthe package capacitance 218 (FIG. 2D) or the combination of the packagecapacitance 218 and the added capacitance 224 (FIGS. 2E-F). Preferably,the value of the inductor 604 is sufficiently large so this parasiticresonance does not shift the oscillation frequency of the oscillator 800from the resonant frequency f₀ of the crystal 214. Accordingly, theparallel combination of the inductor 604 and the crystal 214 should notsubstantially shift the resonant frequency f₀ of the crystal 214, so asnot to change the operating frequency of the oscillator 800. This can beaccomplished by assuring that the parasitic resonance caused by theinductor 604 is lower than the intended resonant frequency of thecrystal 214 by at least approximately a factor of {square root over(0.1)}. For example and without limitation, if the crystal 214 isresonant at 10 MHZ, then the parasitic resonance caused by the inductor604 should preferably be approximately 3 MHZ, or less. For a givencapacitance value, a minimum value for the inductor 604 can bedetermined from Eq. 1. For example, if the crystal 214 has an equivalentcapacitance of 20 pF, then the value of the inductor 604 shouldpreferably be approximately 100 μH (or greater) in order to assure thatthis parasitic resonance is at 3 MHZ or below. Note that if the addedcapacitance 224 (FIGS. 2E-F) is utilized for tuning the crystalresonance, then the total capacitance that is used for in thedetermination of the inductor 604 is the parallel combination of thecapacitor 224 and the capacitor 218.

The resistor 606 dampens out any unwanted parasitic oscillations thatare caused by the addition of the inductor 604. The parasiticoscillations correspond to the parasitic resonance that was describedabove for the inductor 604. It is important to suppress these unwantedoscillations even if the parasitic oscillation frequency is far removedfrom the intended oscillation frequency because the parasiticoscillations will divert signal power from the intended oscillationfrequency. Additionally, parasitic oscillations will frequency mix withintended oscillation frequency and generate spurious signals in theoutput oscillator signal 821, which reduces overall spectral purity ofthe oscillator signal 821.

The value of the resistor 606 should be sufficiently large to suppressthe unwanted oscillation modes caused by the inductor 602. However, theresistor 606 should be no larger than necessary as the resistor 606generates unwanted thermal noise that increases with the resistancevalue according to Eq. 4. The thermal noise of the resistor 606increases the phase noise of the oscillator output signal 821 just likethe bias resistors 810, and therefore defeats the purpose of theinductor circuit 602 if the resistor 606 is too large. As such, theresistor 606 should be no larger than the bias resistors 810, which areapproximately 10 k ohms for some applications. In embodiments, theresistor 606 is a potentiometer (i.e. variable resistor), which allowsfor a variable amount of resistance to be efficiently added to orsubtracted from the inductor circuit 602.

4. External Inductor Determination

As stated above, in embodiments of the invention, the inductor 604 isselected so that the parasitic resonance that is caused by the inductor604 is approximately {square root over (0.1)} of the frequency of thedesired resonance of the crystal 214. The following discussion andequations provide mathematical support for this determination.

Referring to FIG. 2F, the parallel resonance for the crystal 214 occursat the frequency where the admittance of the series resonant circuit 217cancels the admittance of (C_(P) 218∥C_(ADD) 224). Assuming in theequations below that C_(P)=(C_(P) 218∥C_(ADD) 224), then the parallelresonance is determined by the equation 5 below: $\begin{matrix}{{\omega_{p} = \sqrt{\omega_{s}^{2} + \frac{1}{C_{p}L_{M}}}}{where}} & {{Eq}.\quad 5} \\{\omega_{s} = \frac{1}{L_{M}C_{M}}} & {{Eq}.\quad 6}\end{matrix}$

When the external inductor circuit 602 is included as in FIG. 6, andignoring the series resistor 606, then it can be shown that the parallelresonance becomes: $\begin{matrix}{\omega_{p} \approx {\omega_{s} + {\frac{1}{2}\frac{C_{M}}{C_{p}\left( {1 - \frac{\omega_{parasitic}^{2}}{\omega_{p}^{2}}} \right)}}}} & {{Eq}.\quad 7}\end{matrix}$

where ω_(parasitic) represents the (unwanted) low frequency resonancethat is caused by the external inductor 604 resonating with C_(P). Basedon Eq. 7 it is desirable that: $\begin{matrix}{\frac{\omega_{parasitic}^{2}}{\omega_{p}^{2}} \leq 0.1} & {{Eq}.\quad 8}\end{matrix}$

According to Equation 8, it is preferable that the frequency of theparasitic resonance is approximately {square root over (0.1)} of thefrequency of the desired resonance, or lower. Stated another way, theparasitic resonance is preferably lower than the frequency of thedesired resonance by at least approximately a factor of {square rootover (10)}. The result is that the effect of the external inductor 604on the parallel resonance of the crystal 214 will be less than thetolerance of the additional capacitor 224, which is typically 5-10% ofthe capacitor 224 value.

5. Other Applications

The noise reduction invention described herein has been discussed inreference to a crystal oscillator. However, the noise reductioninvention is not limited to crystal oscillators. The noise reductioninvention is applicable to other oscillator circuit configurations,including oscillator circuits that use other types of resonators, suchas discrete circuit elements. Additionally, the noise reductioninvention is applicable to other (non-oscillator) active circuits thatcan benefit from a low frequency feedback path that shorts-out thermalnoise. The application of this noise reduction invention to these otheractive circuits will be understood by those skilled in the relevant artsbased on the discussions given herein, and are within the scope andspirit of the present invention.

6. Conclusion

Example embodiments of the methods, systems, and components of thepresent invention have been described herein. As noted elsewhere, theseexample embodiments have been described for illustrative purposes only,and are not limiting. Other embodiments are possible and are covered bythe invention. Such other embodiments will be apparent to personsskilled in the relevant art(s) based on the teachings contained herein.Thus, the breadth and scope of the present invention should not belimited by any of the above-described exemplary embodiments, but shouldbe defined only in accordance with the following claims and theirequivalents.

What is claimed is:
 1. A method of reducing phase noise at an output ofan oscillator having an active device, the method comprising the stepsof: (1) causing said active device to oscillate at a resonant frequency;and (2) providing a DC feedback path across output terminals of saidactive device.
 2. The method of claim 1, further comprising the step of:(3) biasing said active device using at least one resistor.
 3. Themethod of claim 2, further comprising the step of: (4) shorting-outthermal noise that is generated by said at least one resistor, therebyreducing phase noise at said output of said oscillator.
 4. The method ofclaim 1, wherein said oscillator includes a resonator connected inparallel with said active device, the step (2) further comprising thestep of connecting said DC feedback path across said resonator.
 5. Themethod of claim 1, further comprising the step of: (3) suppressing atleast one oscillation associated with said DC feedback path.
 6. Themethod of claim 1, further comprising the step of: (3) tuning saidresonant frequency to compensate for a shift in frequency associatedwith said DC feedback path.
 7. The method of claim 6, wherein step (3)further comprises the step of adjusting a capacitance coupled to saidactive device.
 8. A differential oscillator circuit, comprising: aresonator having a resonant frequency; an active device, coupled to saidresonator, having a differential output that oscillates at said resonantfrequency; an active bias circuit that provides DC bias for said activedevice; and a DC feedback path coupled to said active device andconnected in parallel with said resonator, whereby said DC feedback pathshorts-out thermal noise associated with said active bias circuit. 9.The differential oscillator circuit of claim 8, wherein said resonatoris a crystal resonator.
 10. The differential oscillator circuit of claim8, wherein said active device includes a pair of cross-connectedtransistors that oscillate at said resonant frequency.
 11. Thedifferential oscillator circuit of claim 10, wherein said pair oftransistors are connected such that a gate of a first transistor isconnected to a drain of a second transistor, a gate of said secondtransistor is connected to a drain of said first transistor, said drainsof said pair of transistors forming said differential output of saiddifferential oscillator circuit.
 12. The differential oscillator circuitof claim 11, wherein said pair of transistors are cross-connectedthrough a pair of capacitors so as to prevent lock-up.
 13. Thedifferential oscillator circuit of claim 8, wherein said active biascircuit includes at least one pair of biasing resistors.
 14. Thedifferential oscillator circuit of claim 8, wherein said DC feedbackpath is connected across said differential output of said active device.15. The differential oscillator circuit of claim 14, wherein saidresonator is connected across said differential output of said activedevice.
 16. The differential oscillator circuit of claim 8, wherein saidDC feedback path includes a resistor for damping at least one parasiticoscillation associated with said DC feedback path.
 17. The differentialoscillator circuit of claim 8, further comprising a pair of capacitorscoupled to said differential output of said differential oscillatorcircuit, said pair of capacitors capable of compensating for a shift infrequency associated with said DC feedback path.
 18. The differentialoscillator circuit of claim 8, wherein said DC feedback path includes aninductor having a value that does not shift said resonant frequency ofsaid resonator.